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Vacant Spaces

Problem 1

Take 18 cards, one of which is the Q, shuffle them and give 10 to East and 8 to West.

Who is more likely to have the Q? It's East, of course.

Problem 2

Now take 26 cards, one of which is the Q, shuffle them and give 13 to East and 13 to West. But I'm going to give you some extra information. 5 of West's cards are clubs and 3 of East's cards are clubs. That means there are only 8 cards in the West hand that you don't know about and 10 cards in the East hand that you don't know about.

Who is more likely to have the Q? Again it's East. Problem 1 and problem 2 are essentially the same.

A real example

On the following hand you are on a contract of 2 and you need to decide how to play the trump suit.

Vacant Spaces in Bridge

With a 9 card the odds a slightly in favour of cashing the A and K hoping that the Q falls. The alternative play of cashing the A and finessing on the second round isn't normally the best way to play this suit combination.

But let me give you some extra information. Suppose I told you that West started with 5 clubs and East started with 3 clubs. That means that West has 8 cards you don't know about and East has 10. Who is more likely to have the Q now?

It's still a very close decision on this hand but I hope you can see that as you gain more information about the oppositions' cards it can alter how you might play.

Between Hands
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